In recent years, as a technique for a sensor to sense an identification target to identify what the identification target is like based on observed data obtained from the sensor, there is known such a technique that a certain probability distribution model is assumed to identify the identification target according to the Bayes' decision rule (refer to, e.g., patent document 1).
Under the assumption that the observed data each follow a single Gaussian distribution, the exponential functions multiplied by a certain constant K: K exp(−z), are compared to one another to thereby enable pattern recognition. This pattern recognition can be realized by the comparison between the numbers of (ln K−z) produced by applying a logarithm to the function and hence there is no need to calculate an exponential function in an identification device. It is to be noted herein that ln K is a constant.
Here, a single Gaussian distribution is unsuitable to data that follow a multi-modal distribution and therefore has disadvantages of limited applications. This problem with the multi-modal distribution, however, can be improved by introducing Gaussian mixture distributions expressed by the following formula which means a weighted sum of Gaussian distributions.
                              ∑          n                ⁢                                  ⁢                              K            n                    ⁢                      exp            ⁡                          (                              -                                  z                  n                                            )                                                          [                  Formula          ⁢                                          ⁢          1                ]            
The patent document 1: Japanese unexamined patent application publication No. 2005-267570